Aircraft: B737
Phase of flight: Cruise
Anomaly: Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Flight Deck / Cabin / Aircraft Event Smoke / Fire / Fumes / Odor

The situation happened on leg 1 on the second day of a 4 day sequence. We departed ZZZ for ZZZ1. As the First Officer I completed both the interior checklists and performed the exterior inspection. I noticed during the walk around that one of the red navigation lights was inoperative. When I got back to the flight deck I confirmed that it was previously written up and had been deferred in the AML. No other issues were noted during the preflight. The Captain was the Pilot Flying and I was the Pilot Monitoring. We departed ZZZ on Runway XXL. The takeoff and departure were uneventful. Weather was clear with unrestricted visibility. The climb was continued until we leveled off at FL340. At approximately XA:13Z; I started to smell something. It smelled like burning plastic. At the same time I noticed the smell the Captain asked 'Do you smell that?' Before replying we both saw smoke coming from the 'FL' button on the transponder located on the center console. At this time we both we executed the items for 'Smoke; Fire; or Fumes'; donned our oxygen masks and established crew communication. At that point the Captain gave me both aircraft control and the radios so he could focus on the abnormal. While I monitored the autopilot the Captain continued with the 'Smoke; Fire; or Fumes' checklist. I confirmed with him that the proper switches were being turned off in accordance with the checklist. We noticed that the smoke and fumes were decreasing and did not need to run the 'Smoke or Fumes Removal' checklist. While the Captain attempted to locate the transponder circuit breaker to isolate the problem he noticed that the 'ELEC PANEL LIGHTS AFT/CENTER' circuit breaker located at the base of the front of the center pedestal was popped. We were confident the problem had been isolated and the Captain informed me that he was about 90% sure we were going to divert but he wanted to check with company to see if we were missing anything. We quickly realized that a step in the checklist had us turn off the internet and he would be unable to use the crew phone app to communicate with the Dispatcher. The Captain then took the radios back and attempted to get phone patch with the Center Controller. The controller was unable to give us the phone patch but was able to relay information. After communicating through the controller and using ACARS; it was decided that we would divert to ZZZ2. The Captain notified ATC and informed Center we wanted to divert to ZZZ2. The controller asked if we want ARFF (aircraft rescue firefighting) and the Captain said yes. The Captain then gave me back the radios so that he could run more checklists. The Captain continued with the checklists the controller asked what runway we wanted to land on. The Captain and I agreed that we wanted the longest runway due to the fact we would be landing overweight. I then requested Runway XXR. I got the airplane set up for an ILS approach to XXR. I started the descent into ZZZ2 while the Captain finished checklists and briefed the passengers and Flight Attendants. Then the Captain told me that he ran the 'Non Routine Landing Considerations' checklist and that the passengers and flight attendants had been briefed. He talked about the heavy weight landing and did a landing assessment. He asked if I had anything to add or could think of anything else we might need to do before landing. I told him that I think we had covered everything and I had nothing else to add. He then briefed the approach and took aircraft control. We completed both the descent and before landing checklists. After landing we cleared the runway at taxiway. I relayed to ARFF that unless they see anything abnormal from the outside our plan was to continue taxing to gate. They informed us that they did not see any unusual readings on thethermal scan. ARFF followed us to the gate. The Captain had me make a PA to the passengers that we would be taxing to gate and they would be accommodated after deplaning. The taxi and engine shutdown at the gate was uneventful. At the gate we were met by a member of the company Flight Office and he asked if we needed to be checked out at the hospital. We both said we did not require medical attention and that no more than a few seconds went by that we breathed in fumes before getting on oxygen. He then told us that he was pulling us off the remainder of the trip and could positive space home. The Captain completed writing up items in the AML. We then debriefed when it was just the two of us left on the airplane. I told him I thought maybe I could have done more to help. He said I did what he needed by flying the airplane and communicating with ATC while he ran the appropriate checklists and backed him up in his decision making process. We both agreed that we handled the situation in the way we are trained to handle abnormal at the school house. The cause was smoke coming from the 'FL' button on the transponder located on the center console. B737-800 First Officer reported a fumes event in the flight deck during cruise resulting in a diversion.